Calculation of transformer winding resonances by a specialized finite element method employing substructures

A method for the calculation of transformer winding resonances is derived which utilizes a specialized finite-element method to compute a 'dynamic' impedance matrix. By modeling the high-frequency leakage field and conductor eddy currents the major sources of internal damping are included. The impedance matrix can be integrated for conventional transient analysis programs based on an equivalent-circuit approach. A substructuring technique in combination with the highly regular winding geometry is used to reduce computational requirements in the finite-element solution. The method is verified by comparison with measurements. Damping causes a shift of resonant frequencies and determines resonant amplitudes. Both effects show up well in the numerical results.<>